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%I #4 Oct 12 2012 14:54:50
%S 1,1,4,1,6,16,1,8,22,92,1,12,34,188,716,1,14,40,248,976,4928,1,18,52,
%T 392,1616,9504,44864,1,20,58,476,1996,12560,61048,348176,1,24,70,668,
%U 2876,20448,104168,658192,3608080,1,30,88,1016,4496,37440,200768
%N A Lucas-Binet triangle read by rows: t(n,m)=((( 1 + Sqrt[Prime[n]]))^m + (( 1 - Sqrt[Prime[n]]))^m)/2.
%C Row sums are: {1, 5, 23, 123, 951, 6207, 56447, 424335, 4394527, 67853311, ...}.
%D Arthur Benjamin and Jennifer J. Quinn, Fibonacci and Lucas Identities through Colored Tilings, Utilitas Mathematica, Vol 56, pp. 137-142, November, 1999. http://www.math.hmc.edu/~benjamin/papers.html
%F t(n,m)=((( 1 + Sqrt[Prime[n]]))^m + (( 1 - Sqrt[Prime[n]]))^m)/2.
%e {1},
%e {1, 4},
%e {1, 6, 16},
%e {1, 8, 22, 92},
%e {1, 12, 34, 188, 716},
%e {1, 14, 40, 248, 976, 4928},
%e {1, 18, 52, 392, 1616, 9504, 44864},
%e {1, 20, 58, 476, 1996, 12560, 61048, 348176},
%e {1, 24, 70, 668, 2876, 20448, 104168, 658192, 3608080},
%e {1, 30, 88, 1016, 4496, 37440, 200768, 1449856, 8521216, 57638400}
%t Binet[n_, m_] = ((( 1 + Sqrt[Prime[n]]))^m + (( 1 - Sqrt[Prime[n]]))^m)/2; a = Table[Table[ExpandAll[Binet[n, m]], {m, 1, n}], {n, 1, 10}]; Flatten[a]
%K nonn,tabl
%O 1,3
%A _Roger L. Bagula_ and _Gary W. Adamson_, Jul 23 2008
%E Edited by _N. J. A. Sloane_, Aug 01 2008
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